>>70
For the size of observable universe. There is nothing after it.
Okay, so such a system with N equal to all the informational content that can be stored in our universe, you're claiming that such N+1 cannot ``exist''.
My question to you would be why do you think this particular universe exists? Why this particular size? Why these particular ``laws of physics''?
My personal opinion on this is that the universe is isomorphic to some system which can be described formally and maybe such systems are even enumerable (so in your beloved set theoretic way I would say that the cardinality of the set of all universes is at least countably infinite (I'm not claiming that any such universe is infinite or that it require non-computational laws!)), although wether they are truly enumerable is unknown (but all Turing Machines are).
If you're going to claim that no other such formal systems (and thus universes) exist, you will have to justify why exactly only this particular instance with these particular rules exists.
If you're going to claim that others may exist, but that their number is finite, you will have to justify why you chose a maximum number of such systems (remember, they do not exist within our universe, they are universes themselves, so the argument that N(as previously mentioned) is the maximum number cannot hold as there can be an universe which can hold N+1 information).
While your argument is fine for systems we can practically implement within our own universe, it cannot hold for more abstract systems (such as other possible universes).
I suppose you could claim that you're a full-on solipsist and the physical reality does not exist in any way or form and that your mind's states are not supervenient to physical states within this universe and if you do that, I cannot argue with you as changing your mind through physical means also means destroying your current state of mind and thus would not be proof to yourself (it can only be proof for a third party).